Tension Amd Temperature Coefficients of the Resistivity of Some Metals Amd Alloys
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University of Ghana http://ugspace.ug.edu.gh TENSION AMD TEMPERATURE COEFFICIENTS OF THE RESISTIVITY OF SOME METALS AMD ALLOYS BY VICTOR KODZO MAWU®NA^‘3i A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF PHILOSOPHY IN PHYSICS AT THE UNIVERSITY OF GHANA, LEGON AUGUST, 1997 University of Ghana http://ugspace.ug.edu.gh (f 352717 TU 672. - t o fyq. THtCsr Roort University of Ghana http://ugspace.ug.edu.gh This work is dedicated to : Evelyn, Derrick and Fafa University of Ghana http://ugspace.ug.edu.gh DECLARATION Except for references to the work of other people, this thesis is the work of the author's own research under the supervision of Professor J. K. A. Amuzu. It has neither in part nor whole been presented elsewhere for the award of a degree. VICTOR KODZO MAWUENA PROF. J.K.A. AMUZU (STUDENT) (SUPERVISOR) DATE DATE University of Ghana http://ugspace.ug.edu.gh PREFACE I thank the Almighty God for making it possible for this work to come out successfully. It was not easy coming out with this work. I owe Prof. J. K. A. Amuzu, my supervisor an incalculable debt of gratitude. I will always remember him for his encouragement and good supervisory skills. I wish to thank my co-supervisors; Prof. R. D. Baeta and Dr. R. Kwaajo for their useful suggestions ana contributions. The kind assistance received from other lecturers of the department is greatly appreciated. My appreciation also go to the laboratory technicians for their contributions in making this work a success. This is an opportunity for me to express my sincere gratitude to my friends, colleagues and all others who in diverse ways have helped to bring this work to a successful completion. Finally, I wish to thank Mr. N. F. Anku for typing this work neatly. Victor Kodzo Mawuena August, 1997 University of Ghana http://ugspace.ug.edu.gh ABSTRACT An attempt has been made to study the effects of tensile stress and temperature on the resistivity of some metals and alloys. The specimens include; copper, constantan, manganin, tantalum and minalpha. The strain coefficient of resistivity dp , rate of increase of fractional resistivity with stress of gde resistance (gauge factor (K)) were determined for copper, constantan, manganin and tantalum. For constantan, ae is found to be highest for a sample of Qde diameter 0.19 mm and lowest for diameter 0.31mm. Tantalum has the highest K-value hence it is the material expected to give relatively the highest strain sensitivity in strain gauges. Minalpha has, however, shown the greatest extent of scatter. University of Ghana http://ugspace.ug.edu.gh LIST OF SYMBOLS USED AND THEIR MEANINGS resistivity Applied tensile stress Poisson's ratio Gruneisen’s constant Gauge factor (coefficient of strain sensitivity of resistance) Temperature (°C) Curie Temperature University of Ghana http://ugspace.ug.edu.gh CONTENTS Page Abstract • i List of Symbols used and their meaning .................. ii CHAPTER ONE : INTRODUCTION ............................... 1 1.1 : Importance of strain gauges ........ 1 1.2 : Types of strain gauges .................. 2 1.3 : Temperature compensation in the strain gauge 3 1.4 : The self-temperature-compensating strain gauge 5 1.5 : Some earlier works .................... 6 1.6 : The Present Work 7 CHAPTER TWO : THE EFFECT OF STRESS AND TEMPERATURE ON THE RESISTIVITY OF METALS.................. 9 2.1 : The effect of stress on the resistivity of metals .................................. 9 2.2 : Effect of dimensional change on the resistance of a wire under strain ...... 10 2.3 : Derivation of gauge (or K-) factor ..... 12 2.4 : Calculation of strain coefficient of resistivity for metals ................... 13 2.5 : Temperature dependence of resistivity of metals ..................................... 15 2.6 : Resistivity and the crystal lattice .... 18 2.7 : Lattice irregularities: effect of of temperature ......................... 18 2.8 : Dissolved atoms and Matthiessen's rule .. 20 University of Ghana http://ugspace.ug.edu.gh CHAPTER THREE : APPARATUS, MATERIALS AND EXPERIMENTAL PROCEDURES 22 3.1 : Introduction 22 3.2 : The resistivity-stress (g-o) apparatus 22 3.3 : The resistivity-temperature (g-T) apparatus 23 3.4 : Construction of the lid of the oven .... 24 3.5 : Materials 24 3.6 : Experimental procedures 25 3.7 : Measurement of change of resistivity (p) with stress (cr) ....................... 25 3.8 : Measurement of change of resistivity (g) with temperature (T) 26 CHAPTER FOUR : RESULTS AND DISCUSSIONS ................ 27 Introduction 27 4.1 : The behaviour of metals under stress ... 27 4.2 : Results from the present study ..... 28 4.3 : Strain coefficient of specific resistivity Ofi gds 30 4.4 : K-factors 36 4.5 : Effect of temperature on resistivity 37 CHAPTER FIVE : CONCLUSIONS 39 References . 41 University of Ghana http://ugspace.ug.edu.gh CHAPTER ONE INTRODUCTION The principle on which strain gauges operate is the well established effect of the change in resistivity due to the imposition of stress. It is clear, therefore, that this present work which studies stress and temperature coefficient of the resistivity of constantan, manganin, copper, tantalum and minalpha is indeed a study of the strain gauge effect. In this introductory chapter, therefore, we devote some attention to reviewing this effect. 1.1 IMPORTANCE 0? STRAIN GAUGES Owing to advancing technology, structural parts require careful consideration for reasons of economy, safety, weight and appearance. This calls for an intensive knowledge of the behaviour of individual parts under stress. Essentially, it is important to (investigate designed structural parts under all stress conditions. ] jThis is useful in all design work. By doing this, it becomes I I possible to match the various components of the entire construction. Various methods exist for obtaining such I , | information. One such important method involves the use of the 'strain gauge. It is however, worth nothing that the diversity of ^train gauges allows several applications even in other disciplines 'such as chemistry and medicine. 1 University of Ghana http://ugspace.ug.edu.gh The use of strain gauges has several advantages over other methods of studying the effect of stress on structural parts. These are: i. the comparatively simple handling; ii. measurements are possible even under dynamic load; iii. good and suitable adaptability to test problem; iv. a large number of measuring systems are cheaply and readily installed; v. largely free of of maintenance and having only little effect on the test object; and vi. measurements can also be made on moving parts or in liquids. By cementing a strain gauge onto the object to be tested, any strain in the test object is transmitted to the strain gauge. The strain causes a proportional change in the resistance of the strain gauge. This change in resistance is related to the strain by a sensitivity-factor, K, which depends on the materials from which the strain gauge is made. 1.2 TYPES OF STRAIN GAUGES There are four major types of strain gauges namely, (i.) flat wire strain gauges; (ii) wrapped around wire strain gauges; (iii) foil strain gauges; and (iv.) semi-conductor strain gauges. Further classification is made according to their arrangement and application. 2 University of Ghana http://ugspace.ug.edu.gh For wirs gauges, wire is either wound around a piece of carrier material or flat in a meander form. With the former design, low grid dimensions are accomplished. However, its disadvantage lies in unfavourable creep behaviour. Due to high dynamic loads which may occur in use, the electrodes are welded to the measuring wire with great care. The use of the strip metal enables the weld to have a particularly high vibration resistance which consequently provides long life for itself (the weld) and the electrodes. Two main disadvantages exist in forming a single wire into a grid. First, each conductor of the grid will lack complete strain transmission, since each turnaround, or enaloop, acts like the end of a single shot bonded filament. Secondly, the enaloop represents a small but significant length of bonded wire at right angles to the desired measuring axis, which will make the grid somewhat responsive to transverse strains. The loss in overall performance that results from forming a single long conductor into a grid is most significant for very short grids, since these contain a greater number of endloops, and the incompletely strained segments at the end of each line represent a greater percentage of the individual strand lengths. 1.3 TEMPERATURE COMPENSATION IN THE STRAIN GAUGE As mentioned earlier, the bonded wire strain gauge is unique among scientific tools because of its versatility. Besides its fundamental use for measuring strains as such, the strain gauge can 3 University of Ghana http://ugspace.ug.edu.gh be adapted to measure loads, torques, pressures, vibrations, and numerous other physical quantities, limited principally by the imagination of the user. Wire resistance strain gauges are now being employed at temperatures ranging from far below zero to close to the melting point of steel (Perry and Lissner, 1955), in locations of zero relative humidity and completely submerged in water and subjected to a number of other adverse environmental conditions. Adequate temperature compensation is an absolute necessity for accurate measurement of static strains with all presently available bonded wire strain gauges. The need for temperature compensation of strain gauges arises from two factors. First, there is the fact that the resistance of most wires changes with temperature. A second temperature effect occurs if the thermal coefficient of expansion of the strain gauge wire is different from that of the structure to which it is bonded. Thus, even if the strain gauge wire had a zero temperature coefficient of resistance, it would still be subject to false strain indications with temperature unless it had the proper coefficient of expansion. If such a gauge were constructed so that it was completely free of temperature errors when bonded to steel, it would be greatly in error if bonded to aluminium or some other metal with a different thermal coefficient of expansion.